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On the Solution of the Boltzmann Transport Equation with Relaxation Time Approximation
Author(s) -
Fogarassy B.
Publication year - 1963
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.19630031217
Subject(s) - boltzmann equation , scalar (mathematics) , relaxation (psychology) , convection–diffusion equation , work (physics) , tensor (intrinsic definition) , integral equation , boltzmann constant , collision , physics , mathematical analysis , classical mechanics , mathematics , statistical physics , quantum mechanics , geometry , computer science , psychology , social psychology , computer security
In a previous paper [1] a solution of the Boltzmann transport equation in ascending powers of the external perturbations is derived for some very general conditions. In the present work a study is made of the higher‐order magnetic field terms arising in this solution, and also the limits of validity of the relaxationtime approximation are considered. In the present work it appears that the collision integral can only be replaced by a relaxation time tensor when the solution of the transport equation can be approximated by the first‐order terms. Finally it is shown that, for special scattering mechanisms, this relaxation time tensor reduces to a scalar, and under these conditions the approximation has a much wider applicability.